Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.

Answer 1

for y = ax^2 + bx + c, the x of the vertex is -b/(2a)
so for h = -16t2 + v0t + h0 , the t of the vertex is -v0/-32 = v0/32
h = -16(v0^2/1024) + (v0)^2 + h0
= -v0/32 + v0^2 + h0

vertex is (v0/32 , -v0/32 + v0^2 + h0)

check my algebra, I did not write it out first.

Answer 2

Recall that for ax^2+bx+c the vertex lies at (-b/2a, (4ac-b^2)/4a)

Now just plug in your coefficients